Detailed computer-assisted comparative analysis of protein sequences and gene arrangement in positive-strand and double-stranded RNA viruses was used to propose evolutionary scenarios and to outline a new, phylogenetic taxonomy of these viruses. Higher taxa of RNA viruses (orders and classes) were proposed based on phylogenetic trees for highly conserved proteins and on comparison of genome organization. The unusual genome organization of two families of positive-strand RNA viruses, namely closteroviruses and astroviruses, was revealed in collaboration with the respective experimental groups. Closteroviruses are a group of plant RNA viruses with unusually large genomes. It was shown that in addition to the core of replicative genes typical of a number of groups of positive-strand RNA viruses, closteroviruses possess several unique genes. These include the leader papain-like thiol protease which was first predicted by computer analysis and subsequently demonstrated experimentally. A unique feature of closteroviruses is a duplication of the coat protein gene which also has been initially discovered by computer and then experimentally. Astroviruses are a group of animal viruses that are only distantly related to the so-called picorna-like supergroup. A unique feature of astroviruses, given the relatively large genome size (> 7 kilobases), is the absence of a gene for RNA helicase. In spite of the major differences in amino acid sequences and genome organization, both closteroviruses and astroviruses utilize the same, unusual mechanism of genome expression, namely programmed ribosomal frameshifting upstream of the RNA-dependent RNA polymerase gene. The study of these virus families has significantly broadened the scope of genome organizations and expression strategies known to exist in positive-strand RNA viruses. Analysis of several genes of iridoviruses and poxviruses was performed as part of the collaboration with experimental laboratories. Genes coding for putative GTPases related to the bacterial MutT proteins and for a specific type of Zn finger proteins were found in both virus groups. Genes for a protein homologous to DNA-binding HMG proteins, DNA helicase and the largest subunit of the DNA-dependent RNA polymerase were identified in iridoviruses. Analysis of the phylogenetic trees for DNA helicases and RNA polymerases has led to the conclusion that iridoviruses and poxviruses have evolved independently from cellular genes.